Question $4($Energy Equation$)$

$4\mathrm{.}1$ A centrifugal pump draws water from Reservoir A through a single suction pipe and

discharges into Reservoir $B$ through a pipe system consisting of a $150mm$ diameter pipe

over the first $100m,$ and a $200mm$ pipe over the remaining $100m,$ as shown in Figure $6$

below. The centreline of the pump is $5m$ below the water level in the suction reservoir and

$20m$ below that in the receiving reservoir. The delivery rate of the pump is $\frac{301}{s}.$

Considering all energy losses, determine:

a$)$ The pressure head supplied by the pump;

b$)$ The power required if the pump has an efficiency of $78\%$ and

c$)$ Draw the hydraulic grade line $($the sketch need not be drawn to scale but should

indicate values at each change in gradient$)$ between the water levels in the two

reservoirs.

The entrance and exit are sharp $(k=0\mathrm{.}5$ and $1$ respectively$)$; the enlargement is sudden

$(k=0\mathrm{.}57)$; and frictional coefficient through the pipeline is $f=0\mathrm{.}008.$

Figure $5$